REFINED BPS STATE COUNTING FROM NEKRASOV'S FORMULA AND MACDONALD FUNCTIONS
REFINED BPS STATE COUNTING FROM NEKRASOV'S FORMULA AND MACDONALD FUNCTIONS
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DOI：
10.1142/s0217751x09043006
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发表时间：
2009-05-10
影响因子：
1.6
通讯作者：
Kanno, Hiroaki
中科院分区：
文献类型：
--
作者：
Awata, Hidetoshi;Kanno, Hiroaki
本文讨论了局部Calabi-Yau空间上M理论的紧化中Nekrasov的配分函数给出了精细BPS状态计数的生成函数。我们证明了我们之前提出的拓扑顶点（arXiv: help -th/0502061）的改进版本是具有两个等变参数的Nekrasov配分函数的构建块。与Iqbal， Kozcaz和Vafa （arXiv: help -th/0701156）的另一种改进的拓扑顶点相比，我们的改进顶点完全用麦克唐纳对称函数的专一化表示，这与C-2上点的Hilbert格式的等变特性有关。从杨-米尔斯理论几何工程中出现的带有八个增压的网图中，给出了计算配分函数的图解规则。我们的改进顶点在图的翻牌操作下有一个简单的变换规律，这表明Hopf链的同调不变量与Macdonald函数有关。
It has been argued that Nekrasov's partition function gives the generating function of refined BPS state counting in the compactification of M theory on local Calabi-Yau spaces. We show that a refined version of the topological vertex we previously proposed (arXiv:hep-th/0502061) is a building block of Nekrasov's partition function with two equivariant parameters. Compared with another refined topological vertex by Iqbal, Kozcaz and Vafa (arXiv:hep-th/0701156), our refined vertex is expressed entirely in terms of the specialization of the Macdonald symmetric functions which is related to the equivariant character of the Hilbert scheme of points on C-2. We provide diagrammatic rules for computing the partition function from the web diagrams appearing in geometric engineering of Yang-Mills theory with eight supercharges. Our refined vertex has a simple transformation law under the flop operation of the diagram, which suggests that homological invariants of the Hopf link are related to the Macdonald functions.